I really like the Fastmail calendar because it has months on a giant scroll, so one leads seamlessly into the next. It works quite well for me because I really think on a "weeks" basis but knowing the month is still important.
Not in the week view, which makes it super annoying - I often want to move/copy events from one week to the next, and I can't do it through drag and drop, because (like almost every webapp out there) Fastmail app doesn't understand interactions like "scroll by one day only" and "if I drag to the edge of the canvas, it means I want you to scroll it".
Month view, yes, has this nice continuity you mentioned. It also has a ... I can't pin exactly what's wrong, but I almost always get confused which month I'm looking at, because the month name label above the calendar seems to often be off by one month relative to what month is visible on the screen. But the bigger issue is, of course, that in a monthly view, you can hardly fit any useful amount of events.